These notes give an account of a series of lectures at the University of Lecce as well as two at the University of Bari, all during Apri1 1986.
§§115 are based on the thesis [18], of J.F.Voloch, a part from some background remarks and classical interpolations. They deal with the number of points on an algebraic curve over a finite field. The main results of the thesis are also contained in [14], §16 records some classical results on elliptic curves and §17, following Voloch [19], proves the existence of complete karcs form any values of k by taking half the points on anelliptic curve. §§1819 discusses the values of n(2,q), the size of the smallest k art in PG(2,q), and m'(2,q), the size of the second largest complete k art in PC(2,q), the main result of §19 follows a proof of Segre using an improved bound for the number of points on a curve from §§ll and 14. Finally, §20 summarizes the best, known estjmates for $m_2(d,q)$, the irrgest size of k cap in PG(d,q).
Table Of Contents
The maximum number of points on an algebraic curve 
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11 
The deduction of Serre's and Ihara's results from the Riemann hypothesis 
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14 
The essential idea in a particular case 
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47 
Weierstrass points in characteristic zero 
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78 
Fundamental definitions in algebraic geometry 
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811 
The canonical series 
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1011 
The osculating hyperplane of a curve 
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1114 
The generalized Wronskian 
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1517 
Construction of some linear systems 
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1819 
The essential construction 
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1924 
Elliptic curves 
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2425 
Hyperelliptic curves 
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2526 
Plane curves 
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2628 
The maximum number of points on an algebraic curve 
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2829 
Elliptic curves: fundamental aspects 
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3035 
karcs on elliptic curves 
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karcs in 
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4243 
kcaps in 
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4647 
Bibliography 
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4849 
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